Mathematical Modeling of Complex Biological Systems A Kinetic Theory Approach [Hardcover]

This book describes the evolution of several socio-biological systems using mathematical kinetic theory. Specifically, it deals with modeling and simulations of biological systems whose dynamics follow the rules of mechanics as well as rules governed by their own ability to organize movement and biological functions. It proposes a new biological model focused on the analysis of competition between cells of an aggressive host and cells of a corresponding immune system. Proposed models are related to the generalized Boltzmann equation. The book may be used for advanced graduate courses and seminars in biological systems modeling.

This book describes the evolution of several socio-biological systems using mathematical kinetic theory. It is one of the first books to apply mathematical kinetic theory to biological systems. Specifically, it deals with modeling and simulations of biological systems.

ContentsandScienti?cAims The scienti?c community is aware that the great scienti?c revolution of this century will be the mathematical formalization, by methods of applied mathematics, of complex biological systems. A fascinating prospect is that biological sciences will ?nally be supported by rigorous investigation me- ods and tools, similar to what happened in the past two centuries in the case of mechanical and physical sciences. It is not an easy task, considering that new mathematical methods maybeneededtodealwiththeinnercomplexityofbiologicalsystemswhich exhibit features and behaviors very di?erent from those of inert matter. Microscopic entities in biology, say cells in a multicellular system, are characterized by biological functions and the ability to organize their dynamics and interactions with other cells. Indeed, cells organize their dynamics according to the above functions, while classical particles follow deterministic laws of Newtonian mechanics. Cells have a life according to a cell cycle which ends up with a programmed deatl“c